ISEM 2016: Ecological Network Analysis
M.K. Lau (Harvard Forest, Harvard University)
Updated “05 May 2016”
Bipartite Networks
- Community ecology’s gateway to ecological networks
Base Quantities
- L: number of realized links in a network
- I: number of lower trophic level species (e.g. plants, prey)
- J: number of higher trophic level species (e.g. pollinators, parasitoids)
- m: total number of interactions for all species
- \(a_{ij}\): number of interactions between species i from the lower and species j from the higher trophic level, also referred as “link weight”
- \(A_i\) (\(\sum_{j=1}^J a_{ij}\)): total number of interactions of species i from the ower trophic level
- \(A_j\) (\(\sum_{i=1}^I a_{ij}\)): total number of interactions of species j from the higher trophic level
Indices (Unweighted)
- Links per Species
- Connectance
- Cluster Coefficient
- Web Asymmetry
- Number of Compartments
- Extinction Slopes
- Degree Distribution
- Mean Number of Shared Hosts
- Togetherness
- C-Score
- V-Ratio
- Nestedness
Weighted Indices
- Nestedness (WINE)
- Modularity
- Generality
- Vulnerability
- Weighted Linkage Density
- Interaction Evenness
- Interaction Strength Asymmetry
- Niche Overlap
Weighted Indices
- Nestedness
- Modularity
- Generality
- Vulnerability
- Weighted Linkage Density
- Interaction Evenness
- Interaction Strength Asymmetry
- Niche Overlap
Nestedness
Nestedness: Packing Communities
Nestedness: Packing Communities
Measuring Nestedness: Many Metrics
1. Ordering
2. Isocline
3. Deviations
Exercise: Play with matrix ordering
Exercise: Play with matrix ordering
M <- c(rep(1,10),
c(rep(1,4),rep(0,6)),
c(rep(1,3),rep(0,7)),
c(rep(1,2),rep(0,8)),
rep(c(rep(1,1),rep(0,9)),6)
)
M <- matrix(M,nrow=10)
rownames(M) <- paste('P',1:10,sep='')
colnames(M) <- paste('A',1:10,sep='')Exercise: Play with matrix ordering
M## A1 A2 A3 A4 A5 A6 A7 A8 A9 A10
## P1 1 1 1 1 1 1 1 1 1 1
## P2 1 1 1 1 0 0 0 0 0 0
## P3 1 1 1 0 0 0 0 0 0 0
## P4 1 1 0 0 0 0 0 0 0 0
## P5 1 0 0 0 0 0 0 0 0 0
## P6 1 0 0 0 0 0 0 0 0 0
## P7 1 0 0 0 0 0 0 0 0 0
## P8 1 0 0 0 0 0 0 0 0 0
## P9 1 0 0 0 0 0 0 0 0 0
## P10 1 0 0 0 0 0 0 0 0 0Exercise: Play with matrix ordering
M[sample(1:10,10),sample(1:10,10)]## A3 A2 A9 A4 A10 A7 A8 A1 A5 A6
## P4 0 1 0 0 0 0 0 1 0 0
## P6 0 0 0 0 0 0 0 1 0 0
## P2 1 1 0 1 0 0 0 1 0 0
## P5 0 0 0 0 0 0 0 1 0 0
## P7 0 0 0 0 0 0 0 1 0 0
## P8 0 0 0 0 0 0 0 1 0 0
## P3 1 1 0 0 0 0 0 1 0 0
## P10 0 0 0 0 0 0 0 1 0 0
## P9 0 0 0 0 0 0 0 1 0 0
## P1 1 1 1 1 1 1 1 1 1 1Exercise: Play with matrix ordering
M[sample(1:10,10),sample(1:10,10)]## A10 A1 A6 A3 A5 A8 A9 A4 A7 A2
## P1 1 1 1 1 1 1 1 1 1 1
## P4 0 1 0 0 0 0 0 0 0 1
## P5 0 1 0 0 0 0 0 0 0 0
## P3 0 1 0 1 0 0 0 0 0 1
## P10 0 1 0 0 0 0 0 0 0 0
## P9 0 1 0 0 0 0 0 0 0 0
## P7 0 1 0 0 0 0 0 0 0 0
## P2 0 1 0 1 0 0 0 1 0 1
## P6 0 1 0 0 0 0 0 0 0 0
## P8 0 1 0 0 0 0 0 0 0 0Exercise: Play with matrix ordering
M[sample(1:10,10),sample(1:10,10)]## A5 A8 A1 A2 A10 A9 A4 A3 A6 A7
## P6 0 0 1 0 0 0 0 0 0 0
## P9 0 0 1 0 0 0 0 0 0 0
## P10 0 0 1 0 0 0 0 0 0 0
## P1 1 1 1 1 1 1 1 1 1 1
## P3 0 0 1 1 0 0 0 1 0 0
## P5 0 0 1 0 0 0 0 0 0 0
## P7 0 0 1 0 0 0 0 0 0 0
## P8 0 0 1 0 0 0 0 0 0 0
## P4 0 0 1 1 0 0 0 0 0 0
## P2 0 0 1 1 0 0 1 1 0 0Testing for Nestedness
- Calculate the nestedness for a given network
- Choose an algorithm to shuffle
- Shuffle the interactions
- Calculate nestedness for the shuffled network
- Repeat a lot, like thousands of times
- Compare the observed to the “null” nestedness values
Testing for Nestedness
obs <- 45
null <- rnorm(1000,65,9)
hist(null,main='')
abline(v=obs)
Testing for Nestedness
z.score <- (obs - mean(null)) / sd(null)
p.value <- length(null[null <= obs])/length(null)
z.score## [1] -2.219385p.value## [1] 0.016
Exercise: Nestedness Analysis
library(bipartite)
data(Safariland)
SafarilandExercise: Nestedness Analysis
## Policana albopilosa Bombus dahlbomii
## Aristotelia chilensis 673 0
## Alstroemeria aurea 0 154
## Schinus patagonicus 0 0
## Berberis darwinii 0 67
## Rosa eglanteria 0 0
## Cynanchum diemii 0 0
## Ribes magellanicum 0 0
## Mutisia decurrens 0 0
## Calceolaria crenatiflora 0 0
## Ruizantheda mutabilis Trichophthalma amoena
## Aristotelia chilensis 110 0
## Alstroemeria aurea 0 0
## Schinus patagonicus 0 0
## Berberis darwinii 0 0
## Rosa eglanteria 6 0
## Cynanchum diemii 0 0
## Ribes magellanicum 0 2
## Mutisia decurrens 0 0
## Calceolaria crenatiflora 0 0
## Syrphus octomaculatus Manuelia gayi
## Aristotelia chilensis 0 0
## Alstroemeria aurea 5 7
## Schinus patagonicus 0 0
## Berberis darwinii 5 0
## Rosa eglanteria 4 0
## Cynanchum diemii 0 0
## Ribes magellanicum 0 0
## Mutisia decurrens 0 0
## Calceolaria crenatiflora 0 0
## Allograpta.Toxomerus Trichophthalma jaffueli
## Aristotelia chilensis 0 0
## Alstroemeria aurea 1 3
## Schinus patagonicus 0 0
## Berberis darwinii 0 0
## Rosa eglanteria 2 0
## Cynanchum diemii 0 0
## Ribes magellanicum 3 0
## Mutisia decurrens 0 0
## Calceolaria crenatiflora 1 0
## Phthiria Platycheirus1 Sapromyza.Minettia
## Aristotelia chilensis 0 4 0
## Alstroemeria aurea 8 1 1
## Schinus patagonicus 0 0 0
## Berberis darwinii 0 0 0
## Rosa eglanteria 0 0 0
## Cynanchum diemii 0 0 0
## Ribes magellanicum 0 0 0
## Mutisia decurrens 1 0 0
## Calceolaria crenatiflora 0 0 0
## Formicidae3 Nitidulidae Staphilinidae
## Aristotelia chilensis 0 0 0
## Alstroemeria aurea 0 0 4
## Schinus patagonicus 0 0 0
## Berberis darwinii 0 0 0
## Rosa eglanteria 0 0 3
## Cynanchum diemii 8 1 0
## Ribes magellanicum 0 0 0
## Mutisia decurrens 0 0 0
## Calceolaria crenatiflora 0 0 0
## Ichneumonidae4 Braconidae3 Chalepogenus caeruleus
## Aristotelia chilensis 1 0 0
## Alstroemeria aurea 0 0 0
## Schinus patagonicus 15 0 0
## Berberis darwinii 0 0 0
## Rosa eglanteria 0 0 0
## Cynanchum diemii 0 2 0
## Ribes magellanicum 0 0 0
## Mutisia decurrens 0 0 0
## Calceolaria crenatiflora 0 0 3
## Vespula germanica Torymidae2 Phthiria1
## Aristotelia chilensis 0 0 0
## Alstroemeria aurea 4 0 1
## Schinus patagonicus 0 0 0
## Berberis darwinii 0 0 0
## Rosa eglanteria 0 0 0
## Cynanchum diemii 0 9 0
## Ribes magellanicum 0 0 0
## Mutisia decurrens 0 0 0
## Calceolaria crenatiflora 0 0 0
## Svastrides melanura Sphecidae Thomisidae
## Aristotelia chilensis 0 0 0
## Alstroemeria aurea 6 1 1
## Schinus patagonicus 0 0 0
## Berberis darwinii 0 0 0
## Rosa eglanteria 0 0 0
## Cynanchum diemii 0 0 0
## Ribes magellanicum 0 0 0
## Mutisia decurrens 0 0 0
## Calceolaria crenatiflora 0 0 0
## Corynura prothysteres Ichneumonidae2
## Aristotelia chilensis 1 0
## Alstroemeria aurea 3 4
## Schinus patagonicus 0 0
## Berberis darwinii 0 0
## Rosa eglanteria 0 0
## Cynanchum diemii 0 0
## Ribes magellanicum 0 0
## Mutisia decurrens 0 0
## Calceolaria crenatiflora 0 0
## Ruizantheda proxima Braconidae2
## Aristotelia chilensis 0 1
## Alstroemeria aurea 4 0
## Schinus patagonicus 0 0
## Berberis darwinii 0 0
## Rosa eglanteria 0 0
## Cynanchum diemii 0 0
## Ribes magellanicum 0 0
## Mutisia decurrens 0 0
## Calceolaria crenatiflora 0 0Exercise: Nestedness Analysis
plotweb(Safariland)
Exercise: Nestedness Analysis
plotweb(Safariland,text.rot=90)
Exercise: Nestedness Analysis
nested(Safariland)## binmatnest2.temperature
## 21.06591Exercise: Nestedness Analysis
nested(Safariland,method='ALL')## binmatnest2.temperature binmatnest discrepancy2.discrepancy
## 19.8363866 5.7626076 14.0000000
## discrepancy C.score checker
## 21.0000000 0.5616097 1.0227920
## NODF2 NODF weighted NODF
## 24.5478036 18.0878553 11.6063738
## wine
## 0.3839732Exercise: Nestedness Analysis
safari.nest <- nestedness(Safariland)
names(safari.nest)## [1] "mat" "n.rows" "n.cols"
## [4] "temperature" "n.nullmodels" "population.size"
## [7] "n.individuals" "binmatnestout" "n.generations"
## [10] "nullmodels" "p.null1" "mean.temp.null1"
## [13] "var.temp.null1" "p.null2" "mean.temp.null2"
## [16] "var.temp.null2" "p.null3" "mean.temp.null3"
## [19] "var.temp.null3" "pack.order.col" "pack.order.row"
## [22] "packed.matrix"Exercise: Nestedness Analysis
unlist(safari.nest[c('temperature')])## temperature
## 5.762608unlist(safari.nest[c('p.null1','p.null2','p.null3')])## p.null1 p.null2 p.null3
## 0 0 0unlist(safari.nest[c('mean.temp.null1','mean.temp.null2','mean.temp.null3')])## mean.temp.null1 mean.temp.null2 mean.temp.null3
## 28.14982 27.33150 18.72031unlist(safari.nest[c('var.temp.null1','var.temp.null2','var.temp.null3')])## var.temp.null1 var.temp.null2 var.temp.null3
## 27.66088 33.82524 36.37121Modularity
Modularity: Eggs in Multiple Baskets
Nestedness Revisited
Nestedness Revisited
Modularity: Eggs in Multiple Baskets
Modularity: Eggs in Multiple Baskets
Modularity
safari.mods <- computeModules(Safariland)Modularity
plotModuleWeb(safari.mods)
Testing Modularity
null.nets <- lapply(1:5,commsimulator,x=Safariland,method='r1')
null.mods <- lapply(null.nets,computeModules)
null.stats <- lapply(null.mods,function(x) slot(x,'likelihood'))
null.stats <- unlist(null.stats)Testing Modularity
obs.mods <- slot(safari.mods,'likelihood')
null.mu <- mean(null.stats)
null.sd <- sd(null.stats)
null.z <- (obs.mods - null.mu) / null.sd
null.p <- length(null.stats[null.stats <= obs.mods])/length(null.stats)
null.z## [1] -2.22749null.p## [1] 0
Nested and Modules
Further reading on bipartite network analysis
- General: https://goedoc.uni-goettingen.de/goescholar/bitstream/handle/1/5837/Dormann.pdf?sequence=1
- Nestedness: https://www.uvm.edu/~ngotelli/manuscriptpdfs/UlrichConsumersGuide.pdf
- Modularity: http://arxiv.org/pdf/1304.3218.pdf
- Null Models: https://www.uvm.edu/~ngotelli/manuscriptpdfs/UlrichEcology.pdf
- Mutualistic Networks: http://press.princeton.edu/titles/10161.html